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In this paper, a new scheme that combines Space-Time Block-Coding (STBC) based on an Alamouti-like scheme and the Least Squares (LS) channel estimation using optimal training sequences in Cyclic-Prefix-based (CP)Single-Carrier (SC) systems is proposed. With two transmit antennas, based on Cramer-Rao lower bound for channel estimation, it is shown that the Periodic Complementary Set (PCS) is optimal over frequency-selective fading channels. Compared with the normal scheme without STBC, 3dB Mean Square Error (MSE) performance gains and fewer restrictions on the length of channel impulse response are demonstrated.